论文信息 - Product and Convolution Theorems for the Fractional Fourier Transform

Product and Convolution Theorems for the Fractional Fourier Transform

The fractional Fourier transform (FRFT) is a generalization of the classical Fourier transform (FT). It has recently found applications in several areas, including signal processing and optics. Many properties of this transform are already known, but an extension of the FT¿s convolution theorem is still missing. The purpose of this paper is to introduce extensions of this theorem, dealing with the FRFT of a product and of a convolution of two functions.

L. B. Almeida

[1] H. Weyl. Quantenmechanik und Gruppentheorie , 1927 .

[2] N. Wiener. Hermitian Polynomials and Fourier Analysis , 1929 .

[3] E. Condon,et al. Immersion of the Fourier Transform in a Continuous Group of Functional Transformations. , 1937, Proceedings of the National Academy of Sciences of the United States of America.

[4] Function spaces between crystal space and Fourier-transform space , 1959 .

[5] V. Bargmann. On a Hilbert space of analytic functions and an associated integral transform part I , 1961 .

[6] V. Namias. The Fractional Order Fourier Transform and its Application to Quantum Mechanics , 1980 .

[7] A. Lohmann. Image rotation, Wigner rotation, and the fractional Fourier transform , 1993 .

[8] H. Ozaktas,et al. Fractional Fourier transforms and their optical implementation. II , 1993 .

[9] Luís B. Almeida. An introduction to the angular Fourier transform , 1993, 1993 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[10] H. Ozaktas,et al. Fractional Fourier transforms and their optical implementation. II , 1993 .

[11] Luís B. Almeida,et al. The fractional Fourier transform and time-frequency representations , 1994, IEEE Trans. Signal Process..